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Ufimsk. Mat. Zh., 2017, Volume 9, Issue 2, Pages 63–93 (Mi ufa376)  

Dicrete Hölder estimates for a certain kind of parametrix. II

A. I. Parfenov

Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk

Abstract: In the first paper of this series we have introduced a certain parametrix and the associated potential. The parametrix corresponds to an uniformly elliptic second order differential operator with locally Hölder continuous coefficients in the half-space. Here we show that the potential is an approximate left inverse of the differential operator modulo hyperplane integrals, with the error estimated in terms of the local Hölder norms. As a corollary, we calculate approximately the potential whose density and differential operator originate from the straightening of a special Lipschitz domain. This corollary is meant for the future derivation of approximate formulas for harmonic functions.

Keywords: cubic discretization, Lipschitz domain, local Hölder norms, parametrix, potential, straightening.

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English version:
Ufa Mathematical Journal, 2017, 9:2, 62–91 (PDF, 576 kB); https://doi.org/10.13108/2017-9-2-62

Bibliographic databases:

Document Type: Article
UDC: 517.518.1
MSC: 35A17
Received: 15.03.2016

Citation: A. I. Parfenov, “Dicrete Hölder estimates for a certain kind of parametrix. II”, Ufimsk. Mat. Zh., 9:2 (2017), 63–93; Ufa Math. J., 9:2 (2017), 62–91

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